Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
Figurate number sequence |
| gptkbp:definedIn |
T_n = n(n+1)/2
|
| gptkbp:first_terms |
1
10 15 3 6 |
| https://www.w3.org/2000/01/rdf-schema#label |
Triangular numbers
|
| gptkbp:property |
The sum of the reciprocals of the triangular numbers converges to 2
The nth triangular number is the sum of the first n natural numbers The sum of two consecutive triangular numbers is a square number The nth triangular number is the binomial coefficient C(n+1,2) The nth triangular number is the number of distinct pairs that can be formed from n+1 objects The nth triangular number is the number of handshakes if n+1 people each shake hands once with every other person The only triangular number that is also a square number greater than 1 is 36 Every even perfect number is a triangular number The sum of the first n triangular numbers is the nth tetrahedral number The difference between the nth and (n-1)th triangular number is n The digital root of a triangular number cycles through 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, ... The difference between consecutive triangular numbers is n |
| gptkbp:relatedTo |
Square numbers
Tetrahedral numbers |
| gptkbp:sequence |
A000217
|
| gptkbp:sumOfFirstNPositiveIntegers |
True
|
| gptkbp:usedIn |
gptkb:Number_theory
Combinatorics |
| gptkbp:visualizes |
Dots arranged in an equilateral triangle
|
| gptkbp:bfsParent |
gptkb:Polygonal_numbers
|
| gptkbp:bfsLayer |
7
|